Laser scanning effect in EEVEE?
I like the effect you have managed with your solution.

You can use a shader in Eevee with the node setup shown.



The inputs on the left control intensity, scan (vertical offset) and focus (sorry I forgot to rename this one).  Thhis can be modded for different scan orientations using the mapping node.

Ad endum

Thought I would offer some explanation on this, it was 0400 hrs when I posted this so I was quite tired.

The magic happens in the mapping node (purple), basically I use the scale vector to squash the texture in the Z direction and scan it using the location vector.  I use a math node to scale the input controls and make them more friendly.

Then pipe this into a a gradient texture and onto the emmision shader. 

I've added some white noise to give that laser effect (although this should probably get its vector from texture-node->object rather than the mapped as white noise shouldn't be squashed.

The rest should be pretty much obvious.